ANGLE DESIGN CALCULATOR (AISC 360-22)

INPUT DATA

Member Geometry (Angle-Section)

L = ft   Member Length

b₁ = in   First Leg Width

b₂ = in   Second Leg Width

t = in   Leg Thickness

Material Properties (ASTM A36)

E = ksi   Elastic Modulus

F_y = ksi   Yield Strength

F_u = ksi   Ultimate Tensile Strength

Axial Loads (Tension Positive, Compression Negative)

N_D = kips   Dead Load Axial Force

N_L = kips   Live Load Axial Force

Bending Loads

w_D = klf   Dead Load (Uniformly Distributed)

w_L = klf   Live Load (Uniformly Distributed)

P_D = kips   Dead Load (Point Load at Midspan)

P_L = kips   Live Load (Point Load at Midspan)

End Restraints

K_min =   Effective Length Factor (Minimum)

LOAD COMBINATIONS (AISC 360-22)

LRFD Load Factors:

w_u = 1.2·w_D + 1.6·w_L = 1.56 klf   Factored Distributed Load

P_u = 1.2·P_D + 1.6·P_L = 22.00 kips   Factored Point Load

N_u = 1.2·N_D + 1.6·N_L = 0.00 kips   Factored Axial Force

ASD Load Factors:

w_a = w_D + w_L = 0.90 klf   Allowable Distributed Load

P_a = P_D + P_L = 15.00 kips   Allowable Point Load

N_a = N_D + N_L = 0.00 kips   Allowable Axial Force

ACTIONS

M_max = w·L²/8 + P·L/4 = 50.25 kip-ft   Maximum Design Moment

V_max = w·L/2 + P/2 = 11.25 kips   Maximum Design Shear

SECTION PROPERTIES

A_g = b₁·t + b₂·t − t² = 4.75 in²   Gross Area

I_x = 21.8 in⁴   Second Moment of Area (x-axis through centroid)

I_y = 12.5 in⁴   Second Moment of Area (y-axis through centroid)

I_xy = 15.3 in⁴   Product of Inertia

I_max = 31.2 in⁴   Maximum Principal Moment of Inertia

I_min = 3.1 in⁴   Minimum Principal Moment of Inertia

θ_p = 32.5 deg   Principal Axis Angle

S_x = 6.2 in³   Elastic Section Modulus (x-axis)

S_y = 4.3 in³   Elastic Section Modulus (y-axis)

r_x = 2.14 in   Radius of gyration (x-axis)

r_y = 1.62 in   Radius of gyration (y-axis)

r_min = 0.81 in   Minimum radius of gyration (about principal axis)

DESIGN CHECKS (AISC 360-22)

Tension Strength (Chapter D)

A_g = 4.75 in²

P_n = F_y·A_g = 171.0 kips   Nominal Tension Capacity

φ_t = 0.90   Resistance Factor (LRFD)

φ_tP_n = 153.9 kips   Design Tension Strength (LRFD)

P_n/Ω_t = 102.4 kips   Allowable Tension Strength (ASD)

Tension Check: Tension_ratio = |N|·φ_tP_n⁻¹ = 0.000

Compression Strength (Chapter E)

L_c = K_min·L·12 = 240 in   Effective Length

r_min = 0.81 in   Minimum Radius of Gyration

λ = L_c/r_min = 296.3   Slenderness Parameter

F_e = π²·E/λ² = 0.33 ksi   Euler Buckling Stress

F_cr = 0.877·F_e = 0.29 ksi   Critical Buckling Stress

P_n = F_cr·A_g = 1.4 kips   Nominal Compression Capacity

φ_cP_n = 1.3 kips   Design Compression Strength (LRFD)

P_n/Ω_c = 0.8 kips   Allowable Compression Strength (ASD)

Compression Check: Compression_ratio = |N|·φ_cP_n⁻¹ = 0.000

Bending Strength (Chapter F)

M_n = F_y·S_max = 93.8 kip-ft   Nominal Moment Capacity (Strong Axis)

φ_b = 0.90   Resistance Factor (LRFD)

φ_bM_n = 70.3 kip-ft   Design Moment Strength (LRFD)

Bending Check: Bending_ratio = M_max/(φ_bM_n) = 0.715

Combined Axial and Bending (Chapter H)

P_u/(φ_cP_n) = 0.000

M_u/(φ_bM_n) = 0.715

Interaction Check: Interaction_ratio = P_u/(φ_cP_n) + M_u/(φ_bM_n) = 0.715

Shear Strength (Chapter G)

A_v = b_max·t = 3.00 in²   Shear Area

V_n = 0.6·F_y·A_v = 64.8 kips   Nominal Shear Strength

φ_vV_n = 58.3 kips   Design Shear Strength (LRFD)

Shear Check: Shear_ratio = V_max/(φ_vV_n) = 0.193

Deflection Check (Serviceability)

δ_max = 5·w_L·L⁴/(384·E·I_max) + P_L·L³/(48·E·I_max) = 0.54 in

δ_limit = L/360 = 0.67 in

Deflection Check: Deflection_ratio = δ_max/δ_limit = 0.81

Compact Section Check (AISC Section B4)

λ_pf = 0.38·√(E/F_y) = 9.6   Limiting λ for compact flange

λ_pl = 0.56·√(E/F_y) = 14.1   Limiting λ for compact leg

λ₁ = b₁/t = 12.00   Slenderness ratio (first leg)

λ₂ = b₂/t = 8.00   Slenderness ratio (second leg)

Section Classification: Compact

RESULTS